In Triangle ABC, BP is perpendicular to the side AC, <A = 60° <C = 45, AB = 6cm, 1) what is the length of AP
2) find BP
3) find the area of ABP
4) what is the area and perimeter of the triangle ABC
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Answer:
We have
(
AC
AQ
)=
9
3
=
3
1
(
AB
AP
)=
10.5
3.5
=
3
1
In ΔAPQ & ΔABC
(
AC
AQ
)=(
AB
AP
)
& ∠PAQ=∠BAC
Thus ΔAPQ∼ΔABC by SAS criterion.
Hence (
AC
AQ
)=(
BC
PQ
) (by cpst)
⇒
3
1
=(
BC
4.5
)
⇒BC=13.5cm.
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